The 980X isn't even a Sandy Bridge chip, so will perform much worse in Dolphin (and, in fact, anything which uses a maximum of four or fewer cores, which is most things) than the 2600 at the same clock rate... but it's frequency is higher, so it won't actually be that far behind.

OS: Windows 10 64 bit Professional
CPU: Intel i5 4670K @3.4GHz... for now @4.6GHz with a quick and dirty (yet stable) OC. May get faster in a bit before the end of time.
RAM: 16GB (Down from 24 GB after some was given to siblings)
GPU: Radeon Vega 56

In the benches ive seen, the clock to clock performance difference is about 10% to Sandy bridge, another 10% to ivy bridge, another 10% to Haswell. So yeah the single core performance is going to be an issue for Dolphin. I will have to test it against my 3770 system.

I assumed the performance gain was somehow a byproduct of Haswell adding AVX2, gather-scatter, BMI1, BMI2, ABM, and FMA3 instruction support. The last 4 being responsible is unlikely though, considering AMD chips also have had those instructions for some time.

AVX2 isn't even used in Dolphin. Gathers aren't either, and are actually slower than doing every load separately. BMI1 isn't used significantly (not sure if I ever finished my patch to add it, but the gain wasn't significant). ABM is AMD-only. FMA3 does matter, but the gain was like 1 or 2 %.

Haswells were fast long before any post-SSSE3 instruction set was even supported in Dolphin. If I had to guess it might be something more subtle, maybe instruction cache-related? Or the 4th execution pipe? But I really don't know...